Jessica is 12 years younger than Michael. Michael and Jessica first met 3 years ago. Two years ago, Michael was 3 times older than Jessica. How old is Michael now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Jessica. Let Michael's current age be $m$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $m = j + 12$ Two years ago, Michael was $m - 2$ years old, and Jessica was $j - 2$ years old. The information in the second sentence can be expressed in the following equation: $m - 2 = 3(j - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = m - 12$ . Substituting this into our second equation, we get the equation: $m - 2 = 3($ $(m - 12)$ $ -$ $ 2)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 2 = 3m - 42$ Solving for $m$ , we get: $2 m = 40$ $m = 20$.